We show that the Cauchy integral operator is bounded from $H^p(R^1)$ to $h^p(R^1)$ (local Hardy space). To prove our theorem we shall introduce generalized atom and consider a variant of "$Tb$ theorem".
"The Cauchy integral operator on Hardy space." Hokkaido Math. J. 37 (2) 389 - 398, May 2008. https://doi.org/10.14492/hokmj/1253539561